Example of a weighted algebra \(\mathcal L_p^w(G)\) on an uncountable discrete group
type: Item
instance of: scholarly article
title: Example of a weighted algebra \(\mathcal L_p^w(G)\) on an uncountable discrete group
zbMATH Open document ID: 1165.43005
author: Yulia Kuznetsova
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-13T00:00:00Z
review text: Let \(G\) be a locally compact group. The author considers the question when a weighted \(L_p\)-space on \(G\) (denoted here by \(L_p^w(G)\)) is a Banach algebra under the convolution multiplication. She shows that for any discrete free group such a weight exists, provided \(1\leq p\leq 2\) (so that \(G\) need not be \(\sigma\)-compact). If the group in question is uncountable, then no such weight can exist, if \(p>2\). She also shows that if \(G\) is amenable and \(L^w_p(G), p>1\), is an algebra for some weight, then \(G\) is \(\sigma\)-compact.
reviewed by: Wiesław Tadeusz Żelazko
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 22D05
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 5553645
zbMATH Keywords: \(L_p\)-conjecture
zbMATH Keywords: group algebra
zbMATH Keywords: locally compact group
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.006
OpenAlex ID: W2011270430
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DOI: 10.1016/J.JMAA.2008.12.006
description: scientific article; zbMATH DE number 5553645